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• W2003467148 abstract "Low order differential equations typically have solutions which represent homoclinic or heteroclinic orbits between singular points in the phase plane. These orbits occur when the stable manifold of one singular point intersects or coincides with its unstable manifold, or the unstable manifold of another singular point. This paper investigates the persistence of these orbits when small dispersion is added to the system. In the perturbed system the stable manifold of a singular point passes through an exponentially small neighbourhood of a singular point and careful analysis is required to determine whether a homoclinic or heteroclinic connection is achieved." @default.
• W2003467148 created "2016-06-24" @default.
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• W2003467148 date "1991-06-01" @default.
• W2003467148 modified "2023-09-25" @default.
• W2003467148 title "On the existence of homoclinic and heteroclinic orbits for differential equations with a small parameter" @default.
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• W2003467148 doi "https://doi.org/10.1017/s0956792500000449" @default.
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